Template:Pointclasses

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Revision as of 01:39, 28 January 2023 by alpha>Indicwiki (Created page with "{{navbar|Pointclasses}} {| class="wikitable" style="text-align: center;" |- !colspan=2| {{nobold|Lightface}} !colspan=2| Boldface hierarchy|Boldface...")
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Lightface Boldface
Σ0
0
= Π0
0
= Δ0
0
(sometimes the same as Δ0
1
)
Σ0
0
= Π0
0
= Δ0
0
(if defined)
Δ0
1
= recursive
Δ0
1
= clopen
Σ0
1
= recursively enumerable
Π0
1
= co-recursively enumerable
Σ0
1
= G = open
Π0
1
= F = closed
Δ0
2
Δ0
2
Σ0
2
Π0
2
Σ0
2
= Fσ
Π0
2
= Gδ
Δ0
3
Δ0
3
Σ0
3
Π0
3
Σ0
3
= Gδσ
Π0
3
= Fσδ
Σ0
= Π0
= Δ0
= Σ1
0
= Π1
0
= Δ1
0
= arithmetical
Σ0
= Π0
= Δ0
= Σ1
0
= Π1
0
= Δ1
0
= boldface arithmetical
Δ0
α
recursive)
Δ0
α
countable)
Σ0
α
Π0
α
Σ0
α
Π0
α
Σ0
ωCK
1
= Π0
ωCK
1
= Δ0
ωCK
1
= Δ1
1
= hyperarithmetical
Σ0
ω1
= Π0
ω1
= Δ0
ω1
= Δ1
1
= B = Borel
Σ1
1
= lightface analytic
Π1
1
= lightface coanalytic
Σ1
1
= A = analytic
Π1
1
= CA = coanalytic
Δ1
2
Δ1
2
Σ1
2
Π1
2
Σ1
2
= PCA
Π1
2
= CPCA
Δ1
3
Δ1
3
Σ1
3
Π1
3
Σ1
3
= PCPCA
Π1
3
= CPCPCA
Σ1
= Π1
= Δ1
= Σ2
0
= Π2
0
= Δ2
0
= analytical
Σ1
= Π1
= Δ1
= Σ2
0
= Π2
0
= Δ2
0
= P = projective